Hiroki Masuda, Kyusyu University

Tentative Title:
"Non-Gaussian quasi-likelihood estimation of jump processes"

Abstract:
We consider parametric estimation of stochastic differential equations 
with jumps when the process is discretely observed at high frequency. 
Since the exact transition probability generally does not have a closed 
form, the maximum likelihood estimation cannot be of practical use, and 
therefore we are forced to resort to some other feasible estimation 
procedure. The Gaussian quasi-likelihood estimation (based on fitting 
local mean and local variance, and known to be asymptotically efficient 
in case of diffusion processes) is one of natural candidates as in the 
case of diffusions, and actually it leads to asymptotically normally 
distributed estimator. However, the Gaussian quasi-likelihood estimation 
loses much asymptotic efficiency in the presence of jumps. We propose 
yet another quasi-likelihood estimation procedure based on non-Gaussian 
type contrast functions, and show that the resulting estimator may 
exhibit better theoretical performances than the one based on the 
Gaussian quasi-likelihood.